(CNN) -- Lawmakers expressed shock - and a desire for more information - after Gen. John Allen, the top American military commander in Afghanistan, was ensnared in a growing scandal that brought down CIA director David Petraeus at the end of last week.

"Disturbing is the word that has come to my mind since all of this has come to light," Rep. Debbie Wasserman Schultz of Florida, the chairwoman of the Democratic National Committee, said on CNN's "Starting Point with Soledad O'Brien."

"Really, I think it goes without saying if you're the director of the CIA, if you are a four-star general in the United States Army, that you have to hold yourself to a higher standard. And you can't put yourself in a compromising position," the Florida Democrat said.

Wasserman Schultz made the remarks after authorities announced that Allen is under investigation for allegedly sending inappropriate messages to Jill Kelley, a woman who has been linked to the Petraeus scandal.

Allen, who is the commander of NATO's International Security Assistance Force, has denied any wrongdoing, a senior defense official said.

Rep. Tom Price, R-Ga., said the thickening scandal has prompted a lot of "whys" -- including why Congressional leaders with oversight over intelligence and homeland security weren't informed of potentially compromised information. The National Security Act of 1947 stipulates the "congressional intelligence committees are kept fully and currently informed on the intelligence activities of the United States."

"Congress' role is oversight. There will be oversight hearings, but the real question is about this administration. Why the opaqueness? Why the transparency? What did they know, when did they know it?" Price asked, also on "Starting Point."

"There are real questions that need to be answered," he continued. "This administration and these individuals need to answer questions about whether there was any compromise in American intelligence or security."

Wasserman Schultz agreed that "an investigation has to be done," and that Congressional leaders on the House and Senate intelligence committees could have been told sooner about investigations into Petraeus' extramarital affair. But she cautioned against injecting politics into a situation with national security ramifications.

"Let's not have this spiral downward into something that just becomes more politics. We just came off an election," she said.